(eng): We design an algorithm for computations of quasiconvex hulls of isotropic compact sets in in the space of 2×2 real matrices. Our approach uses a recent result by the first author [Adv. Calc. Var. 8 (2015) 43--53] on quasiconvex hulls of isotropic compact sets in the space of 2×2 real matrices. We show that our algorithm has the time complexity of O(N log N) where N is the number of orbits of the set. Finally, we outline some applications of our results to relaxation of L-ifnifitive variational problems.